They led 1-0 at Whaddon Road in injury time, only to end up losing.
The boot was on the other foot this time as Brighton recovered from an early goal down to win with two late strikes of their own.
Their bid for compensation got off to the worst possible start when they fell behind inside three minutes.
Steve Thomson ran into trouble in midfield and Steve Brooker, on loan from Bristol City, advanced unchallenged to rifle Cheltenham ahead from 25 yards.
Glenn Murray lobbed against the crossbar for Brighton midway through the first half after his partner Nicky Forster set him up, but the home side were booed off at half-time by the lowest league crowd ever at Withdean.
Brighton boss Dean Wilkins made a double substitution for the second half, bringing on Joel Lynch for Guy Butters in defence and Tommy Fraser for Kerry Mayo in midfield.
And the changes paid off, Lynch playing a pivotal part in Brighton's recovery on his return from a six-week absence with a hamstring injury.
He launched a long ball out of defence for Murray to fire the equaliser in the 80th minute - his third goal in four starts since a £300,000 move from Rochdale last month.
Lynch completed the comeback with three minutes left, heading in following a scramble from a corner.
The Cheltenham players were furious but the assistant referee ruled that the ball had crossed the line.
Afterwards, Cheltenham chief Keith Downing said: "It was debatable to say the least. It is hard to take because I felt we had ridden the storm until Brighton's late goals."